Though I also speculate that it is the largest number of leading zeros for the hash of any known input.

Here is a list of the top 10 hashes to date, followed by the block number in which they appear. It is based on the "hashPrev" values of a recent blockchain. And of course, the first is the made-up value from the genesis block.[('0000000000000000000000000000000000000000000000000000000000000000', -1), ('00000000000000001e8d6829a8a21adc5d38d0a473b144b6765798e61f98bd1d', 125552), ('0000000000000000629981ebad88aafb5856e6663998d1083d74008be66a384a', 133316), ('00000000000000011ac23090a91a9297e8cb27c6d81cea9fc429fd37468d509e', 128456), ('000000000000000166b3b12f3e8928897fa5241985e75a9d31945dc2d22a39c8', 130557), ('0000000000000001e4646f3b4841707b62ecf7412ebc0bdbd2538e745d474a79', 133047), ('0000000000000001f2542ad9420bb538ffebd2e872d1dcbed233d07dc5eb0e01', 132103), ('00000000000000022d118b8a6b54cf261f3fb854b32f57d70545ad566e4adc7f', 132750), ('0000000000000002739d5a374b95e8bd7f5b7c810d07407924385b2181586dc6', 131384), ('0000000000000002ed549896e4571ab6ec7d805741038cb8dac97d4c2917c729', 128687)]

Followup question: what is the exact input for this hash? I guess it would be best to provide it as an easy-to-copy-paste value, i.e. in some standard encoding like base64, so it is easy for folks outside of the bitcoin community to validate it.

Well, 67 bits. I'd say that if a password hash algorithm produced exactly 67 bits (i.e. sha256(sha256(input)), truncated after the 67th bit), we have to date demonstrated a crack of a particular value (all zeros).

Followup question: what is the exact input for this hash? I guess it would be best to provide it as an easy-to-copy-paste value, i.e. in some standard encoding like base64, so it is easy for folks outside of the bitcoin community to validate it.

I wrestled through the non-standard use of little-endian hashes and input values in bitcoin, and dug out the block input which results in this tiny tiny hash output. I documented it all as an example in the wiki:

Note that you have to convert it to binary, hash it with SHA-256 twice, then reverse the bytes to get the value you compare with the target. Then convert back to hex to match the blockexplorer representation of the hash:

Then again, do remember the BTC network has GPU power equaling 146 petaFLOPS (146,407 gigaFLOPS) average as of July 2011. That's over a hundred times faster than the Tianhe-1 supercluster that held the #1 position on the top500.org list of the world's most powerful computers.